Question

AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.

Answer 1

In ΔCAD and ΔCBE
CA = CB  ...(Isosceles triangles)
∠CDA = ∠CEB = 90°
∠ACD = ∠BCE =  ...(common)
Therefore, ΔCAD ≅ ΔCBE  ...(AAS criteria)
Hence, CE = CD
But, CA = CB
⇒ AE + CE = BD + CD
⇒ AE = BD.